The structure of the compressible reacting mixing layer: Insights from linear stability analysis

Abstract

Previous investigations have demonstrated that a compressible reacting mixing layer can develop two instability modes in addition to the more common central mode that exists unaccompanied in incompressible nonreacting flows. These two additional modes are termed “outer” because of their association with the fast and slow free streams. Numerical simulations have shown that mixing layers dominated by outer modes have a lower global reaction rate in comparison to a flow structure governed by the central mode. Therefore, the presence of these modes has important consequences for applications in supersonic combustion. Results are presented from a parametric study of the compressible reacting mixing layer’s regime space using linear stability analysis. The focus of our work is to develop a better understanding for the combined effects of compressibility, heat release and the ratios of density, equivalence, and velocity on the instability characteristics of each mode and on the structure predicted to result in a turbulent reacting mixing layer.

Measurements in the annular shear layer of high subsonic and under-expanded round jets

“…It was also suggested that for M C > 1.0 the isentropic model for U C described above was inappropriate and in fact at high M C turbulent eddies in the fast/slow streams could be convected at fast and slow speeds, respectively. This had first been noted by Lessen et al (1966) (see also Day et al 1998) using linear instability analysis of laminar shear layers at high supersonic conditions, showing that at high M C (>2), as well as the standard instability convecting at U C (the 'central mode'), additional instability modes travelling at speeds associated with the fast/slow streams, respectively ('outer' modes), could be identified. Data on turbulence statistics were only forthcoming when non-intrusive laser-based instrumentation was applied.…”

Triple point shear-layers in gaseous detonation waves

“…Boundary conditions for G on both sides of the free-stream are obtained by using equations (32) and (30).…”

“…Day et al, 32 related the attenuation of the disturbance growth in diffusion controlled, reactive mixing layers to the reduction of the density weighted vorticity,ρdū/dη| η=0 . It should be noted that Day et al 32 used a flame sheet model so that the effect of the reactivity was not included.…”

Spatial linear stability of a hypersonic shear layer with nonequilibrium thermochemistry

“…The effect of chemical reaction and heat release has also received significant attention predominantly for combustion applications, particularly in the effect on the outer modes. At supersonic convective Mach numbers, additional fast and slow "outer" unstable modes are found, [10][11][12] whose velocities are supersonic relative to the slow and fast speed streams, respectively. Shin and Ferziger 13 performed an inviscid spatial stability analysis with simplified one-step kinetics and found that the supersonic modes become less unstable with increasing the Mach number and more unstable with increasing heat release.…”